arnie has between 300 and 400 stickers in her collection. when she divided them into groups of 4, 5, or 9, there is always one sticker left over. how many stickers does arnie's collection contain?
can some of you show the solution to this problem?
numbers, which when divided by 4 leave a remainder of 1
301, 305, 309, 313, 317, 321, 325, 329, 333, 337, 341, 345, 349, 353, 357, 361, 365, ...
numbers, which when divided by 5 leave a remainder of 1
301, 306, 311, 316, 321, 326, 331, 336, 341, 346, 351, 356, 361, 366, 371, ...
numbers which when divided by 9 leave a remainder of 1
307, 316, 325, 334, 343, 352, 361, ...
Ahhh, found 361 in all 3 lists
This method works but is very time consuming.
For a general solution , look up "Chinese Remainder Theorem". There are
several good youtube videos for this type of problem, but it requires some
understanding of modular arithmetic.
btw, the smallest positive integer that works here is 181, found by the
Chinese Remainder Theorem.
Once you have that , to get more just do
181 + k(4*5*9), where k is a natural number
e.g. 181 + 6(4*5*9) = 1261 <------ test it